Curvature-induced bound states for a delta interaction supported by a curve in R-3

0185693 - UJF-V 20027187 RIV DE eng J - Journal Article
Exner, Pavel - Kondej, Sylwia
Curvature-induced bound states for a delta interaction supported by a curve in R-3.
Annales Henri Poincare. Roč. 3, č. 5 (2002), s. 967-981. ISSN 1424-0637. E-ISSN 1424-0661
R&D Projects: GA AV ČR IAA1048101
Keywords : quantum wave-guides * operators
Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders
Impact factor: 1.054, year: 2002

We study the Laplacian in L-2(R-3) perturbed on an infinite curve Gamma by a delta interaction defined through boundary conditions which relate the corresponding generalized boundary values. We show that if Gamma is smooth and not a straight line but it is asymptotically straight in a suitable sense, and if the interaction does not vary along the curve, the perturbed operator has at least one isolated eigenvalue below the threshold of the essential spectrum.
Permanent Link: http://hdl.handle.net/11104/0082076